TY - JOUR

T1 - From Infection Clusters to Metal Clusters

T2 - Significance of the Lowest Occupied Molecular Orbital (LOMO)

AU - Tsuji, Yuta

AU - Yoshizawa, Kazunari

N1 - Funding Information:
The authors thank two anonymous reviewers for their helpful comments. This work was supported by KAKENHI grants (numbers JP17K14440 and JP17H03117) from the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT) through the MEXT projects Integrated Research Consortium on Chemical Sciences, Cooperative Research Program of Network Joint Research Center for Materials and Devices and Elements Strategy Initiative to Form Core Research Center, and by JST-CREST JPMJCR15P5 and JST-Mirai JPMJMI18A2. The computations in this work were primarily performed using the computer facilities at the Research Institute for Information Technology, Kyushu University. Y.T. is grateful for a JSPS Grant-in-Aid for Scientific Research on Innovative Areas (Discrete Geometric Analysis for Materials Design, grant number JP20H04643, and Mixed Anion, grant number JP19H04700).

PY - 2021/1/19

Y1 - 2021/1/19

N2 - In this paper, the nature of the lowest-energy electrons is detailed. The orbital occupied by such electrons can be termed the lowest occupied molecular orbital (LOMO). There is a good correspondence between the Hückel method in chemistry and graph theory in mathematics; the molecular orbital, which chemists view as the distribution of an electron with a specific energy, is to mathematicians an algebraic entity, an eigenvector. The mathematical counterpart of LOMO is known as eigenvector centrality, a centrality measure characterizing nodes in networks. It may be instrumental in solving some problems in chemistry, and also it has implications for the challenge facing humanity today. This paper starts with a demonstration of the transmission of infectious disease in social networks, although it is unusual for a chemistry paper but may be a suitable example for understanding what the centrality (LOMO) is all about. The converged distribution of infected patients on the network coincides with the distribution of the LOMO of a molecule that shares the same network structure or topology. This is because the mathematical structures behind graph theory and quantum mechanics are common. Furthermore, the LOMO coefficient can be regarded as a manifestation of the centrality of atoms in an atomic assembly, indicating which atom plays the most important role in the assembly or which one has the greatest influence on the network of these atoms. Therefore, it is proposed that one can predict the binding energy of a metal atom to its cluster based on its LOMO coefficient. A possible improvement of the descriptor using a more sophisticated centrality measure is also discussed.

AB - In this paper, the nature of the lowest-energy electrons is detailed. The orbital occupied by such electrons can be termed the lowest occupied molecular orbital (LOMO). There is a good correspondence between the Hückel method in chemistry and graph theory in mathematics; the molecular orbital, which chemists view as the distribution of an electron with a specific energy, is to mathematicians an algebraic entity, an eigenvector. The mathematical counterpart of LOMO is known as eigenvector centrality, a centrality measure characterizing nodes in networks. It may be instrumental in solving some problems in chemistry, and also it has implications for the challenge facing humanity today. This paper starts with a demonstration of the transmission of infectious disease in social networks, although it is unusual for a chemistry paper but may be a suitable example for understanding what the centrality (LOMO) is all about. The converged distribution of infected patients on the network coincides with the distribution of the LOMO of a molecule that shares the same network structure or topology. This is because the mathematical structures behind graph theory and quantum mechanics are common. Furthermore, the LOMO coefficient can be regarded as a manifestation of the centrality of atoms in an atomic assembly, indicating which atom plays the most important role in the assembly or which one has the greatest influence on the network of these atoms. Therefore, it is proposed that one can predict the binding energy of a metal atom to its cluster based on its LOMO coefficient. A possible improvement of the descriptor using a more sophisticated centrality measure is also discussed.

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U2 - 10.1021/acsomega.0c04913

DO - 10.1021/acsomega.0c04913

M3 - Article

AN - SCOPUS:85099931022

VL - 6

SP - 1339

EP - 1351

JO - ACS Omega

JF - ACS Omega

SN - 2470-1343

IS - 2

ER -